Group Theory of Circular-Polarization Effects in Chiral Photonic Crystals with Four-Fold Rotation Axes, Applied to the Eight-Fold Intergrowth of Gyroid Nets

TL;DR

This paper uses group theory and scattering matrix calculations to analyze circular polarization effects in chiral photonic crystals with cubic symmetry, revealing transmission properties and optical activity relevant for nanophotonic applications.

Contribution

It provides analytical and numerical insights into polarization-dependent band structure and scattering in chiral photonic crystals with four-fold rotation symmetry, especially applied to Gyroid-based structures.

Findings

All bands along the cubic [100] direction correspond to specific irreducible representations.

Transmission channels for circular polarizations are identified and characterized.

Finite slabs exhibit equal transmission rates and polarization rotation with minimal ellipticity.

Abstract

We use group or representation theory and scattering matrix calculations to derive analytical results for the band structure topology and the scattering parameters, applicable to any chiral photonic crystal with body-centered cubic symmetry I432 for circularly-polarised incident light. We demonstrate in particular that all bands along the cubic [100] direction can be identified with the irreducible representations E+/-,A and B of the C4 point group. E+ and E- modes represent the only transmission channels for plane waves with wave vector along the ? line, and can be identified as non-interacting transmission channels for right- (E-) and left-circularly polarised light (E+), respectively. Scattering matrix calculations provide explicit relationships for the transmission and reflectance amplitudes through a finite slab which guarantee equal transmission rates for both polarisations and vanishing ellipticity below a critical frequency, yet allowing for finite rotation of the polarisation plane. All results are verified numerically for the so-called 8-srs geometry, consisting of eight interwoven equal-handed dielectric Gyroid networks embedded in air. The combination of vanishing losses, vanishing ellipticity, near-perfect transmission and optical activity comparable to that of metallic meta-materials makes this geometry an attractive design for nanofabricated photonic materials.